You have free access to this content

A Monte Carlo study comparing PIV, ULS and DWLS in the estimation of dichotomous confirmatory factor analysis

  1. Steffen Nestler*

Article first published online: 24 APR 2012

DOI: 10.1111/j.2044-8317.2012.02044.x

Issue

British Journal of Mathematical and Statistical Psychology

British Journal of Mathematical and Statistical Psychology

Volume 66, Issue 1, pages 127–143, February 2013

Additional Information

How to Cite

Nestler, S. (2013), A Monte Carlo study comparing PIV, ULS and DWLS in the estimation of dichotomous confirmatory factor analysis. British Journal of Mathematical and Statistical Psychology, 66: 127–143. doi: 10.1111/j.2044-8317.2012.02044.x

Author Information

  1. Johannes Gutenberg University, Mainz, Germany

* Correspondence should be addressed to Steffen Nestler, Westfälische Wilhelms-University, Münster Fliednerstr. 21 Münster 48149, Germany (e-mail: nestler@wwu.de)

Publication History

  1. Issue published online: 17 JAN 2013
  2. Article first published online: 24 APR 2012
  3. Received 17 June 2011; revised version received 31 January 2012

SEARCH

SEARCH BY CITATION

ARTICLE TOOLS

View Full Article with Supporting Information (HTML) Get PDF (610K)

References

  • Angrist, J. D., Imbens, G. W., & Rubin, D. B. (1996). Identification of causal effects using instrumental variables. Journal of the American Statistical Association , 91, 444–455. doi:10.2307/2291629
  • Babakus, E., Ferguson, C. E., & Jöreskog, K. G. (1987). The sensitivity of confirmatory maximum likelihood factor analysis to violations of measurement scale and distributional assumptions. Journal of Marketing Research , 37, 72–141. doi:10.2307/3151512
  • Baum, C. F., Schaffer, M. E., & Stillman, S. (2003). Instrumental variables and GMM: Estimation and testing. Stata Journal , 3, 1–31.
  • Beauducel, A., & Herzberg, P. Y. (2006). On the performance of maximum likelihood versus means and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling , 13, 186–203. doi:10.1207/s15328007sem1302_2
  • Bentler, P. M., & Savalei, V. (2010). Analysis of correlation structures: Current status and open problems. In S. Kolenikov, D. Steinley, & L. Thombs (Eds.), Statistics in the social sciences: Current methodological developments . Hoboken , NJ : Wiley.
  • Bollen, K. A. (1989). Structural equations with latent variables . New York : Wiley.
  • Bollen, K. A. (1996). An alternative two stage least square (2SLS) estimator for latent variables. Psychometrika , 61, 109–121. doi:10.1007/BF02296961
  • Bollen, K. A., & Bauer, D. J. (2004). Automating the selection of model-implied instrumental variables. Sociological Methods and Research , 32, 425–452. doi:10.1177/0049124103260341
  • Bollen, K. A., Bauer, D. J., Christ, S. L., & Edwards, M. C. (2010). An overview of structural equation models and recent extensions. In S. Kolenikov, D. Steinley, & L. Thombs (Eds.), Statistics in the social sciences: Current methodological developments . Hoboken , NJ : Wiley.
  • Bollen, K. A., & Maydeu-Olivares, A. (2007). Polychoric instrumental variable (PIV) estimator for structural equations with categorical variables. Psychometrika , 3, 309–326. doi:10.1007/s11336-007-9006-3
  • Bound, J., Jaeger, D. A., & Baker, R. M. (1995). Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variables is weak. Journal of the American Statistical Association , 90, 443–450. doi:10.2307/2291055
  • Browne, M. W. (1984). Asymptotic distribution free methods in the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology , 37, 127–141.
    Direct Link:
  • Christoffersson, A. (1975). Factor analysis of dichotomized variables. Psychometrika , 40, 5–32. doi:10.1007/BF02291477
  • Christoffersson, A., & Gunsjö, A. (1996). A short note on the estimation of the asymptotic covariance matrix for polychoric correlations. Psychometrika , 61, 173–175. doi:10.1007/BF02296965
  • Dolan, C. V. (1994). Factor analysis of variables with 2, 3, 5 and 7 response categories: A comparison of categorical variable estimators using simulated data. British Journal of Mathematical and Statistical Psychology , 47, 309–326.
    Direct Link:
  • Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika , 43, 521–532. doi:10.1007/BF02293811
  • Flora, D., & Curran, P. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods , 9, 466–491. doi:10.1037/1082-989X.9.4.466
  • Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009). Factor analysis with ordinal indicators: A Monte-Carlo study comparing DWLS and ULS estimation. Structural Equation Modeling , 16, 625–641. doi:10.1080/10705510903203573
  • Genz, A., Bretz, F., Miwa, T., Mi, X., Leisch, F., Scheipl, F., & Hothorn, T. (2011). mvtnorm: Multivariate normal and t distributions. R package version 0.9–9991.
  • Hägglund, G. (1982). Factor analysis by instrumental variables methods. Psychometrika , 47, 209–22. doi:10.1007/BF02296276
  • Hall, A. R. (2005). Generalized method of moments . Oxford : Oxford University Press.
  • Jöreskog, K. G. (1983). Factor analysis as an error-in-variables model. In H. Wainer & S. Messick (Eds.), Principles of modern psychological measurement . Hillsdale , NJ : Lawrence Erlbaum.
  • Jöreskog, K. G. (1994). On the estimation of polychoric correlations and their asymptotic covariance matrix. Psychometrika , 59, 381–389. doi:10.1007/BF02296131
  • Jöreskog, K. G., & Sörbom, D. (1996). LISREL 8: User's reference guide . Chicago : Scientific Software.
  • Kirby, J. B., & Bollen, K. A. (2009). Using instrumental variables to evaluate model specification in latent variable structural equation models. Sociological Methodology , 39, 327–355.
    Direct Link:
  • Kolenikov, S. (2009). Confirmatory factor analysis using confa. Stata Journal , 9, 329–373.
  • Madansky, A. (1964). Instrumental variables in factor analysis. Psychometrika , 29, 105–13. doi:10.1007/BF02289693
  • McDonald, R. P. (1999). Test theory: A unified approach . Mahwah , NJ : Lawrence Erlbaum Associates.
  • Morgan, S. L., & Winship, C. (2007). Counterfactuals and causal inference: Methods and principles for social research . Cambridge : Cambridge University Press.
  • Muthén, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika , 43, 551–560. doi:10.1007/BF02293813
  • Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical and continuous latent variable indicators. Psychometrika , 49, 115–132. doi:10.1007/BF02294210
  • Muthén, B., & Asparouhov, T. (2002). Latent variable analysis with categorical outcomes: Multiple-group and growth modeling in Mplus . Retrieved January 06, 2012, from http://www.statmodel.com/download/webnotes/CatMGLong.pdf
  • Muthén, B., du Toit, S. H. C., & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes . Unpublished manuscript.
  • Muthén, B., & Kaplan, D. (1992). A comparison of some methodologies for the factor-analysis of non-normal Likert variables: A note on the size of the model. British Journal of Mathematical and Statistical Psychology , 45, 19–30.
    Direct Link:
  • Muthén, B., & Satorra, A. (1995). Technical aspects of Muthén's LISCOMP approach to estimation of latent variable relations with a comprehensive measurement model. Psychometrika , 60, 489–503. doi:10.1007/BF02294325
  • Muthén, L., & Muthén, B. (1998). Mplus user guide (Version 3.1). Los Angeles : Muthén & Muthén.
  • Nestler, S., Back, M. D., & Egloff, B. (2011). Psychometrische Eigenschaften zweier Skalen zur Erfassung interindividueller Unterschiede in der Präferenz zum Alleinsein. Diagnostica , 57, 57–67. doi:10.1026/0012-1924/a000032
  • Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika , 44, 443–460. doi:10.1007/BF02296207
  • R Development Core Team (2011). R: A language and environment for statistical computing . Vienna : R Foundation for Statistical Computing.
  • Sargan, J. D. (1958). The estimation of economic relationships using instrumental variables. Econometrica , 26, 393–415.
  • Saris, W. E., Satorra, A., & van der Veld, W. (2009). Testing structural equation models or detection of misspecifications? Structural Equation Modeling , 16, 561–582. doi:10.1080/10705510903203433
  • Savalei, V., & Kolenikov, S. (2008). Constrained vs. unconstrained estimation in structural equation modeling. Psychological Methods , 13, 150–170. doi:10.1037/1082-989X.13.2.150
  • Vale, C. D., & Maurelli, V. A. (1983). Simulating multivariate nonnormal distributions. Psychometrika , 48, 465–471. doi:10.1007/BF02293687
  • Yu, C. Y. (2002). Evaluating cutoff criteria of model fit indices for latent variable models with binary and continuous outcomes (doctoral dissertation). University of California, Los Angeles .
View Full Article with Supporting Information (HTML) Get PDF (610K)